✍ Scribed by George A Gratzer
No coin nor oath required. For personal study only.
Combines the techniques of an introductory text with those of a monograph to introduce the general reader to lattice theory & to bring the expert up to date on the most recent developments. This present edition has been significantly updated & expanded.
General Lattice Theory......Page 4
Copyright Page......Page 5
Contents......Page 8
Preface and Acknowledgements......Page 10
Introduction......Page 12
1. Two Definitions of Lattices......Page 16
2. How to Describe Lattices......Page 24
3. Some Algebraic Concepts......Page 30
4. Polynomials, Identities, and Inequalities......Page 41
5. Free Lattices......Page 47
6. Special Elements......Page 62
Further Topics and References......Page 67
Problems......Page 71
1. Characterization Theorems and Representation Theorems......Page 74
2. Distributive, Standard, and Neutral Elements......Page 153
3. Congruence Relations......Page 88
4. Boolean Algebras R-generated by Distributive Lattices......Page 101
5. Topological Representation......Page 114
6. Distributive Lattices with Pseudocomplementation......Page 126
Further Topics and References......Page 135
Problems......Page 141
1. Weak Projectivity and Congruences......Page 144
3. Distributive, Standard, and Neutral Ideals......Page 161
4. Structure Theorems......Page 166
Further Topics and References......Page 173
Problems......Page 174
1. Modular Lattices......Page 176
2. Semimodular Lattices......Page 187
3. Geometric Lattices......Page 193
4. Partition Lattices......Page 207
5. Complemented Modular Lattices......Page 216
Further Topics and References......Page 233
Problems......Page 239
1. Characterizations of Equational Classes......Page 242
2. The Lattice of Equational Classes of Lattices......Page 251
3. Finding Equational Bases......Page 258
4. The Amalgamation Property......Page 267
Further Topics and References......Page 275
Problems......Page 277
1. Free Products of Lattices......Page 280
2. The Structure of Free Lattices......Page 297
3. Reduced Free Products......Page 303
4. Hopfien Lattices......Page 313
Further Topics and References......Page 318
Problems......Page 321
CONCLUDING REMARKS......Page 326
BIBLIOGRAPHY......Page 331
TABLE OF NOTATION......Page 377
INDEX......Page 380
📜 SIMILAR VOLUMES
In this present edition, the work has been significantly updated and expanded. It contains an extensive new bibliography of 530 items and has been supplemented by eight appendices authored by an exceptional group of experts. The first appendix, written by the author, briefly reviews developments in
<P>"Grätzer’s 'General Lattice Theory' has become the lattice theorist’s bible. Now we have the second edition, in which the old testament is augmented by a new testament. The new testament gospel is provided by leading and acknowledged experts in their fields. This is an excellent and engaging seco
In the first half of the nineteenth century, George Boole's attempt to formalize propositional logic led to the concept of Boolean algebras. While investigating the axiomatics of Boolean algebras at the end of the nineteenth century, Charles S. Peirce and Ernst Schröder found it useful to introduce